Titlebook: Classes of Linear Operators; Israel Gohberg,Marinus A. Kaashoek,Seymour Goldber Book 1993 Birkhäuser Verlag 1993 Mathematik.complex analys

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Unitary Systems and Characteristic Operator Functionsnput-output map or the associated transfer function. In the theory of characteristic operator functions the situation is different. Here the main operator ., which is a contraction, comes first and the characteristic operator function serves as a unitary invariant for ..

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https://doi.org/10.1007/b101825This chapter contains the Stone-Weierstrass theorem and the Gelfand-Naimark representation theorem for commutative Banach algebras with an involution. The latter theorem is used to derive the spectral theorem for a normal operator. The Gelfand-Naimark characterization of a .*-algebra as a closed *-subalgebra of operators is also presented.

Spongy-Bone

Additive Lower-Upper Triangular Decompositions of OperatorsThe decomposition.maybe viewed as the analogue of the additive lower-upper triangular decomposition of a square matrix. In this chapter we study such decomposition for general operators. We begin with the first generalization of the matrix case.

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Block Toeplitz OperatorsThe first three sections of this chapter have an introductory character. Section 2 contains a short introduction to Laurent operators. In Section 3 the first properties of block Toeplitz operators are derived. Sections 4 and 5 develop the Fredholm theory of block Toeplitz operators defined by continuous functions.

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